Question

Point M is the midpoint of vec (AB). If the coordinates of M are (2,8) and the coorclinates of A are (10,12), what are the coortinates of B ?

Answer 1

The coordinates of point B are (-1, 11).

Step-by-step explanation:

To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of the endpoints. We are given that point M is the midpoint of vector (AB), and the coordinates of M are (2,8). The coordinates of A are (10,12).

Let's use the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the given values, we have:

(2,8) = ((10 + x2)/2, (12 + y2)/2)

Simplifying the equation, we get:

(2,8) = (5 + x2)/2, (6 + y2)/2)

Multiplying both sides of the equation by 2, we have:

(4, 16) = (5 + x2, 6 + y2)

Subtracting 5 from both sides of the equation, we get:

(4, 16) - (5, 5) = (x2, y2)

Simplifying the equation, we have:

B = (-1, 11)